Evolution of Bias in Different Cosmological Models

Abstract

We study the evolution of the halo-halo correlation function and bias in four cosmological models (ΛCDM, OCDM, τ CDM, and SCDM) using very high-resolution N -body simulations with dynamical range of ∼ 10, 000 − 32, 000 (force resolution of ≈ 2 − 4h −1 kpc and particle mass of ≈ 10 9 h −1 M ⊙ ). The high force and mass resolution allows dark matter (DM) halos to survive in the tidal fields of highdensity regions and thus prevents the ambiguities related with the "overmerging problem." This allows us to estimate for the first time the evolution of the correlation function and bias at small (down to ∼ 100h −1 kpc) scales.We find that at all epochs the 2-point correlation function of galaxy-size halos ξ hh is well approximated by a power-law with slope ≈ 1.6 − 1.8. The difference between the shape of ξ hh and the shape of the correlation function of matter results in the scale-dependent bias at scales ∼ < 7h −1 Mpc, which we find to be a generic prediction of the hierarchical models, independent of the epoch and of the model details. The bias evolves rapidly from a high value of ∼ 2 − 5 at z ∼ 3 − 7 to the anti-bias of b ∼ 0.5 − 1 at small ∼ < 5h −1 Mpc scales at z = 0. Another generic prediction is that the comoving amplitude of the correlation function for halos above a certain mass evolves non-monotonically: it decreases from an initially high value at z ∼ 3 − 7, and very slowly increases at z ∼ < 1. We find that our results agree well with existing clustering data at different redshifts, indicating the general success of the hierarchical models of structure formation in which galaxies form inside the host DM halos. Particularly, we find an excellent agreement in both slope and the amplitude between ξ hh (z = 0) in our ΛCDM 60 simulation and the galaxy correlation function measured using the APM galaxy survey. At high redshifts, the observed clustering of the Lyman-break galaxies is also well reproduced by the models. We find good agreement at z ∼ > 2 between our results and predictions of the analytical models of bias evolution. This indicates that we have a solid understanding of the nature of the bias and of the processes that drive its evolution at these epochs. We argue, however, that at lower redshifts the evolution of the bias is driven by dynamical processes inside the nonlinear high-density regions such as galaxy clusters and groups. These processes do not depend on cosmology and tend to erase the differences in clustering properties of halos that exist between cosmological models at high z. Subject headings: cosmology: theory -large-scale structure of universe -methods: numerical

The Dark Side of the Halo Occupation Distribution

“…Interestingly, the magnitude of the antibias is considerably smaller than in the higher normalization ( 8 ¼ 1) simulation (see Fig. 7 in Colín et al 1999, as well as Fig. 9 in this paper).…”

“…Figure 9 also shows that the amplitude and shape of the CF at z ¼ 0 are in good agreement with that of the galaxies in the APM survey. As noted by and Colín et al (1999), the close agreement of halo and galaxy correlation functions indicates that the overall clustering of the galaxy population is determined by the distribution of their dark matter halos. Figure 10 shows a comparison of the projected correlation functions:…”

“…clustering of halo samples with maximum circular velocities larger than a given threshold value, which were the focus of the present and other recent studies Colín et al 1999;Neyrinck et al 2004). This type of halo sample should correspond to volume-limited samples of galaxies with luminosities above a certain threshold value because the maximum circular velocity of a halo is expected to be tightly correlated with the luminosity of the galaxy it hosts.…”

“…All the fits for the ÃCDM 80 simulations are performed at r 8 h À1 Mpc, as the CF shape becomes affected at scales larger than 0.1L box (Colín et al 1997(Colín et al , 1999. We also checked this by comparing matter correlation functions in the simulation with the model of Smith et al (2003).…”

“…Nevertheless, despite the apparent complexity, there is evidence that gravitational dynamics alone may explain the basic features of galaxy clustering, at least in the simple case of galaxies selected above a luminosity or mass threshold. Building on several pioneering studies (e.g., Carlberg 1991;Brainerd & Villumsen 1992, 1994a, 1994bColín et al 1997), and Colín et al (1999) used high-resolution N-body simulations that resolved both isolated halos and dark matter substructure within virialized halos to show that the correlation function of galactic halos has a power-law shape with an amplitude and slope similar to those measured in the Automated Plate Measuring (APM) galaxy catalog (Baugh 1996). More recently, Neyrinck et al (2004) showed that dark matter subhalos identified in a different set of dissipationless simulations have a correlation function and power spectrum that matches that of the galaxies in the Point-Source Catalog Redshift survey.…”